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  • Title: Kramers' law for a bistable system with time-delayed noise.
    Author: Goulding D, Melnik S, Curtin D, Piwonski T, Houlihan J, Gleeson JP, Huyet G.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2007 Sep; 76(3 Pt 1):031128. PubMed ID: 17930220.
    Abstract:
    We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than tau, the delayed noise acquires a nonzero mean value and becomes negatively autocorrelated. To account for these effects we define an effective potential and an effective diffusion coefficient of the delayed noise.
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